A Convolution-Based Shearlet Transform in Free Metaplectic Domains
Tarun Kumar Garg, Waseem Z. Lone, Firdous A. Shah, Hatem Mejjaolı
Abstract
The free metaplectic transformation (FMT) is a multidimensional integral transform that encompasses a broader range of integral transforms, from the classical Fourier to the more recent linear canonical transforms. The aim of this study is to introduce a novel shearlet transform by employing the free metaplectic convolution structures. Besides obtaining the orthogonality relation, inversion formula, and range theorem, we also study the homogeneous approximation property for the proposed transform. Towards the culmination, we formulate the Heisenberg and logarithmic-type uncertainty principles associated with the free metaplectic shearlet transform.
Topics & Concepts
ShearletConvolution theoremMathematicsFractional Fourier transformIntegral transformOrthogonalityFourier transformMellin transformConvolution (computer science)Two-sided Laplace transformHartley transformTransformation (genetics)Mathematical analysisPure mathematicsFourier analysisComputer scienceArtificial intelligenceWaveletGeometryGeneArtificial neural networkChemistryBiochemistryMathematical Analysis and Transform MethodsImage and Signal Denoising MethodsDigital Filter Design and Implementation